Chapter 8.3 — Writing the Empirical Paper (and the Abstract Your Poster Carries)

You have, by now, almost everything a paper is made of. You filed a pre-analysis plan (Ch 7.3) and distilled it into the one page the whole project defends — the identification memo of Ch 7.5. You executed the pre-registered specification and built the specification curve (Ch 8.1). You ran column 3 of your threats table for every row, turning each promised defense into an actual robustness result (Ch 8.2). What you have is a folder full of tables, a frozen point estimate, a defensible identifying assumption, and a pile of checks that survived. What you do not yet have is a paper. This chapter is about the last transformation: turning that folder into a piece of prose that a stranger — a busy, skeptical, slightly hostile stranger called a referee — reads in one sitting and comes away believing.

The ASSIP framing — what this chapter’s prose discipline serves. ASSIP’s required terminal deliverable is a research poster and a JSSR abstract, not a full paper (an optional companion paper is available for students who want one — see Lab 8). This chapter is still the binding prose-discipline standard for ASSIP, for two reasons. First, the JSSR abstract that appears on your poster’s title block and in the Journal of Student-Scientists’ Research is a 200–300-word miniature of the introduction this chapter teaches — the same four moves (hook, contribution, “we find” preview, positioning bridge), the same one-sentence-contribution discipline of §3, the same causal-language calibration of §7, compressed to ten sentences. The abstract is an introduction at one-twentieth scale, and a chapter on writing an introduction is a chapter on writing your JSSR abstract. Second, the prose blocks on your poster (the question panel, the design panel, the contribution-and-limits panel — Ch 8.5 §1) are governed by the same arguments-not-transcripts, headline-first, calibrated-verbs disciplines below. Read this chapter as if you were writing a full paper — that is the only way to learn the shape — and at the end of every section ask: and what survives this rule when I compress it to one poster panel or to one of ten abstract sentences? The answers are in PS 8.3, which has been adapted from a “write the introduction and results” assignment to a “write the JSSR abstract and the poster’s results narrative” assignment built on top of this chapter.

Here is the reveal, the thing this whole chapter turns on, stated before the details so you carry it through everything that follows. A paper is not a transcript of what you did; it is an argument for why a reader should believe what you found. Those are different objects. The transcript is chronological and exhaustive — first I downloaded HMDA, then I cleaned it, then I tried three specifications, two of which broke. The argument is logical and ruthlessly selective — here is the question, here is why my design answers it, here is the answer, here is why you cannot easily dismiss it. Beginning writers produce transcripts and wonder why nobody finishes them. The move from transcript to argument is the single most valuable skill this chapter teaches, and almost every rule below is a special case of it.

There is a second reveal layered under the first, and it is the reason Week 5 came before Week 8. You already know how to read a paper as a referee — tables first, identifying assumption second, prose last and skeptically. Writing the paper is just building the object you learned to attack, so that it survives your own Week-5 reading. Every section below maps onto a question your Reader’s-Guide anatomy taught you to ask. The introduction answers “what is the question and why should I care?” The design section answers “what is the identifying assumption, and would it hold?” The results section answers “what is the headline number?” You are not learning a new format. You are learning to write for the reader you already are.

1. The shape of the paper

Empirical-finance papers have a fixed skeleton, and the fixedness is a gift, not a constraint. A referee opening your manuscript knows exactly where to look for each thing, which means you do not get credit for being creative with the order — you only get penalized for hiding the introduction’s contribution in section 4. The standard order is: introduction, literature, data, empirical design / identification, results, robustness, conclusion, with tables and figures threaded through results and robustness and the bibliography at the back. Top journals vary the labels (some fold literature into the introduction, some call the design section “empirical strategy” or “research design”), but the load each section carries is invariant. Learn the loads, not the labels.

The proportions matter as much as the order. A common rookie error is a fifteen-page paper with a one-paragraph introduction and a six-page data section describing every variable in loving detail. Invert that instinct. The introduction is the most-read and most-rewritten part of the paper — many referees decide whether to recommend acceptance from the introduction alone, then read the rest looking for reasons to confirm that snap judgment. The data section, by contrast, should be efficient: enough that the work is reproducible, not so much that it buries the argument. Spend your writing time where the reader spends their attention, and the reader spends it at the front.

One structural principle unifies the whole document: say the important thing first, at every scale. The paper leads with its contribution. The introduction leads with the hook. The results section leads with the headline table. Each paragraph leads with its topic sentence. A reader who quits after the first sentence of any unit should still have learned the most important thing in that unit. This is the opposite of how you were taught to write a mystery-novel essay in high school, building suspense toward a reveal at the end. In a paper, suspense is a bug. The reader is not your entertainment; they are your judge, and you make their job easy by front-loading every verdict.

2. The introduction that promises

The introduction is a promise machine. In roughly four to six paragraphs it must make a specific reader want to read the rest, and it does that by promising — credibly — that the payoff is worth their next twenty minutes. There is a near-canonical structure that the best empirical papers follow almost mechanically, and you should follow it too until you have earned the right to deviate. It has four moves: the hook, the one-sentence contribution, the “we find” preview, and the roadmap. Take them in order.

The hook. The first paragraph names the question and makes the reader care, in that order, fast. It opens with a real-world fact or tension — a number, a puzzle, a policy debate — not with “the literature has long studied.” Maya’s hook is not “fair lending has been studied since the 1970s.” It is closer to: In 2023, mortgage applicants from minority neighborhoods were denied at nearly twice the rate of applicants from white neighborhoods — a gap that persists even among applicants with similar incomes and loan sizes. Whether that gap reflects differential treatment, and whether policy can move it, is both a live regulatory question and an unresolved empirical one. Two sentences and the reader knows the stakes are real, the question is contested, and an answer would matter. The hook earns the reader’s attention with consequence, not with a literature recitation.

The one-sentence contribution. This is the sentence everything else serves, and it deserves its own subsection below — for now, know that it lands in the first or second paragraph and says, in one sentence, what this paper adds that did not exist before you wrote it. Not what you did (“we run a difference-in-differences on HMDA”) but what is now known that was not (“we provide the first causally credible estimate of how state fair-lending examination programs affect the minority–white mortgage-denial gap”). The difference between those two formulations is the difference between a paper that gets read and one that gets desk-rejected.

The “we find” preview. Having promised a contribution, you must immediately pay a deposit on it: tell the reader the answer. A paragraph, usually beginning literally “We find that…” or “Our main result is…,” that previews the headline number, its sign, its rough magnitude, and the key robustness fact. We find that adopting a fair-lending examination program reduces the county-level minority–white denial gap by about 1.8 percentage points, roughly a fifth of the pre-period gap; the effect emerges within two years of adoption, is robust to alternative control groups and clustering, and survives a placebo test that randomly reassigns adoption years. Students resist this. They feel they are “spoiling the ending.” Reread §1: there is no ending to spoil. A referee who has to hunt through nine pages to find out what you found is a referee who is already annoyed with you. Give the number up front; you will spend the rest of the paper earning the right to have stated it.

The roadmap. The introduction’s last paragraph is a short, functional map: “Section 2 positions our work in the literature; Section 3 describes the HMDA data; Section 4 lays out the difference-in-differences design and our identifying assumption; Section 5 presents the main results; Section 6 reports robustness; Section 7 concludes.” A few sentences, no drama. Some venues consider the explicit roadmap old-fashioned, but for a student paper it is a safe, professional default — it signals that you know the genre.

A discipline that spans all four moves: the introduction should be readable by someone who will never read the rest of the paper. A program officer skimming fifty abstracts, a professor deciding whether to assign your paper, a journalist looking for a number to quote — all of them stop at the introduction. Write it so that a reader who stops there walks away with the question, the answer, and the appropriate degree of confidence. If your introduction only makes sense after one has read your results, it has failed at its one job.

3. The one-sentence contribution

Stop and build this sentence on its own, because if you cannot write it, you do not yet have a paper — you have a regression and a hope, the same diagnosis the identification memo gave you about the identifying assumption. The one-sentence contribution is the answer to a question a skeptical reader is entitled to ask and will ask: what is true now, that was not established before you did this work? It is the reason the paper exists. Everything else — the data, the design, the forty robustness checks — is in service of making this one sentence believable, exactly as the whole paper is in service of the identifying-assumption sentence. The two sentences are cousins: one states what you claim to have found, the other states the condition under which the claim is true.

A good contribution sentence usually does one of a small number of recognizable jobs, and naming the job helps you write the sentence. You might be the first to credibly estimate a specific effect (“we provide the first quasi-experimental estimate of…”). You might overturn or qualify an established finding (“we show that the widely cited X effect disappears once Y is accounted for”). You might reconcile two conflicting literatures, measure a mechanism the literature had only speculated about, or bring new data to an old question (“using transaction-level on-chain data, we…”). Pick the job honestly. The fastest way to a referee’s contempt is a contribution sentence that claims the “first” job when three prior papers did the same thing, which is exactly what your literature review is about to either support or expose.

Calibrate the verb to the evidence — this is the causal-language discipline of §7, previewed here because it bites first in this sentence. If your design is a clean staggered DiD with flat pre-trends, you have earned “credibly estimate.” If your design is OLS on observables with a plausible omitted variable you could not rule out, you have not, and your contribution sentence says “document a robust association,” “provide suggestive evidence,” or “establish a new stylized fact” — never “show that X causes Y.” The reading guides of Week 5 trained you to catch authors who overclaim in exactly this sentence. The grader of your paper is running the same check. Match the verb to the design, and run the check on yourself before anyone else does.

A practical test: hand your one-sentence contribution to a classmate who has not seen your project and ask them to tell you, from that sentence alone, what you did and why it matters. If they can, the sentence works. If they ask “wait, what’s the question?” or “is that causal?”, the sentence is doing the introduction’s whole job badly, and no amount of polish on paragraphs four through forty will fix it.

4. The literature review that positions

Here is where most student papers go wrong, and the failure has a name: the annotated bibliography. That is the literature review that reads “Smith (2018) finds A. Jones (2020) finds B. Garcia (2021) finds C. We contribute to this literature.” It is a list. It does the reader no work. It tells them what exists but not where the hole is, and the hole is the only thing the section exists to reveal. A list of prior work is to a literature review what a transcript is to a paper — the raw material, mistaken for the finished argument.

A literature review does exactly one job: it draws a map of what is known so that the gap you fill is visible as a gap. The reader should finish the section able to point at empty space on the map and say “ah — that is what nobody has done, and that is what this paper does.” You build that map by grouping and contrasting, not by enumerating. Cluster the prior work into two or three strands — by question, by method, or by finding — and characterize each strand by what it established and what it could not. “One strand documents the raw denial gap (Bartlett et al.; the HMDA descriptive literature) but cannot separate differential treatment from differential applicant composition. A second strand uses audit studies to isolate treatment but cannot speak to the population-scale effect of policy. We sit at the intersection: population-scale HMDA data and a policy shock that lets us identify a treatment effect.” Now the gap is not asserted; it is constructed, brick by brick, out of the literature itself.

Three rules keep the section honest and sharp. First, every paper you cite should be load-bearing — it either builds part of the map’s wall or marks the edge of the hole. If a citation could be deleted without changing where the gap appears, delete it; a padded literature review signals that you are counting references rather than building an argument. Second, be generous to the work you build on and precise about its limits, never dismissive. “Prior work was wrong” is the voice of someone who has not read carefully and is about to be refereed by the author they just insulted. “Prior work established X under conditions Y; we extend to the case where Y fails” is the voice of someone who belongs in the conversation. Third, position, do not summarize. The reader does not need a book report on each paper; they need to know its coordinate on your map. One sentence per paper, often less, with the contrast doing the work.

This section is also where Weeks 5 and 6 cash out. You read Fama–French, Jegadeesh–Titman, Petersen, Bertrand–Duflo–Mullainathan, the fair-lending and innovation literatures, precisely so you would know which conversations exist and where the live arguments are. A literature review is you reporting back from those conversations and announcing where you intend to speak. Cite primary sources with full bibliographic information per CONVENTIONS §6, and if you cannot verify a citation, tag it [CHECK] rather than fabricate it — a hallucinated reference is the one error a referee can catch in ten seconds and never forgive.

5. Data, design, and results

These three sections are the body of the paper — the place where the promise of the introduction is redeemed with actual evidence. Each has a specific load to carry, and a specific failure mode to avoid.

The data section makes the work reproducible without burying the argument. It names the source and vintage (HMDA LAR, a pinned snapshot date per CONVENTIONS §5), the sample (which years, which units, which filters and why each filter was applied — every exclusion is a potential selection threat, so disclose it), the unit of observation, and the construction of the key variables. It carries one near-mandatory artifact: a summary-statistics table (means, standard deviations, counts, by treatment status where relevant) that lets a reader sanity-check the sample before trusting anything built on it. What the data section does not do is narrate your cleaning ordeal. The reader does not need to know that the 2018 file had a malformed column; they need to know the final sample and how to rebuild it. Put the ordeal in the replication packet (Ch 8.5) and the appendix, not the paper.

The empirical design / identification section puts the identifying assumption front and center. This section is, in large part, your Ch 7.5 identification memo turned into prose, and that is by design — the identifying-assumption paragraph you wrote there becomes this section nearly verbatim. State the specification in the CONVENTIONS §4 form: outcome, treatment, controls, fixed effects, clustering, sample, and the identifying assumption in one sentence. Write the estimating equation explicitly. For Maya, the staggered group-time formulation she committed to:

\text{Gap}_{ct} = \sum_{k \neq -1} \beta_k \,\mathbb{1}[t - G_s = k] + \boldsymbol{\delta}'\mathbf{X}_{ct} + \alpha_c + \lambda_t + \varepsilon_{ct},

where \text{Gap}_{ct} is the county-year minority–white denial gap, G_s is the year state s adopted its examination program, \alpha_c and \lambda_t are county and year fixed effects, and standard errors are clustered by state. Then — and this is the heart of the section — state the assumption that makes \beta_k for k \geq 0 a causal effect rather than a correlation: absent the programs, adopting and never-adopting states’ denial gaps would have moved in parallel. Name the threat, name the design feature that addresses it, in the same breath. This is CONVENTIONS §4 and the entire ethic of the identification memo, now load-bearing in the paper. A design section that says “we control for confounders” instead of naming the assumption has thrown away the one thing that makes the paper credible.

The results section leads with the headline table. Open with the single table that contains your main estimate — for Maya, the overall ATT and the event-time profile from the clean Callaway–Sant’Anna estimator. Walk the reader through it in prose: point at the coefficient, state its sign, its magnitude in units a human can feel (1.8 percentage points, “a fifth of the pre-period gap” — not just a number), and its statistical precision. The cardinal sin here is the “data dump”: a results section that presents eight tables with equal weight and lets the reader find the important one. You found it for them in the introduction; do it again here. Lead with the headline, interpret it economically (is the effect big enough to matter, not just big enough to be significant?), and only then present the supporting and secondary results. Significance is not the same as importance — a coefficient can be three-starred and economically trivial — and your prose must carry the economic interpretation that the stars cannot.

6. Robustness and conclusion

The robustness section converts your threats table into persuasion. You already did the work in Chapter 8.2 — the placebos, the alternative standard errors, the bandwidth and control and sample perturbations, the Oster (2019) \delta for selection on unobservables. The writing task is to present those checks as answers to the specific threats your design section raised, not as a context-free pile of extra regressions. The organizing move is to mirror the threats-and-responses table from your identification memo: each subsection of robustness takes one named threat and shows the check that addresses it, with the residual concern stated plainly. “A reader might worry that the result is driven by anticipation; we re-estimate excluding the year before adoption and the effect is unchanged (Table 5).” That sentence does three things — names the threat, reports the check, states the reassuring result — and it does them in the reader’s order, the order in which they would attack the paper. Robustness sections that persuade are organized around the reader’s doubts, not around the author’s available regressions. Appendix D.3 gives the detailed standard for this; the principle is that a robustness check no one asked for persuades no one, while a check that answers a threat a referee was about to raise disarms the attack before it lands.

The conclusion says what we learned, what we cannot claim, and what comes next. It is not a summary that repeats the introduction — the reader just read the paper; they do not need a recap. It is a recalibration. First, a tight restatement of the finding in its properly hedged form. Second — and this is the part students skip, to their cost — an honest statement of limitations: the residual concerns from your threats table, the populations your sample does not cover, the mechanism you measured an effect on but could not fully open up. The conclusion is where the residual-concern column of your identification memo finally appears in the paper’s prose, and stating it is not weakness; it is the candor that makes a referee trust everything else. Third, “what’s next”: the question your paper opened but did not close, the natural extension, the data that would settle the residual concern. A conclusion that admits limits and points forward reads as the work of someone who sees their project clearly. A conclusion that claims the question is now permanently settled reads as the work of someone who has not yet been refereed.

There is a temptation, in the conclusion, to let the verbs creep back up — to write “this paper proves” or “we have established that” after eleven pages of disciplined hedging. Resist it. The conclusion is the most-quoted part of the paper after the abstract, and a single overclaiming sentence there can undo the calibrated honesty of everything before it.

7. Causal-language discipline

Run a thread back through every section above: the contribution sentence, the design section, the results, the conclusion all live or die on whether you matched your verbs to your evidence. This deserves its own treatment because it is the discipline most often broken and most ruthlessly punished, and because you have been trained to enforce it on others since Week 5.

The rule is simple to state. Your strongest verb is bounded by your weakest assumption. A clean randomized experiment earns “causes,” “increases,” “the effect of.” A quasi-experiment with a testable-and-passed identifying assumption (a DiD with flat pre-trends, an RD with a smooth density) earns “causally estimate,” “the program reduced,” with the assumption named. An observational regression on observables — OLS with a plausible omitted variable you could not rule out — earns only “is associated with,” “predicts,” “is consistent with,” “suggestive of.” A descriptive or predictive study (Sam’s momentum sort, Fama–French) earns “documents,” “captures variation in,” and must not be dressed in causal clothing at all. The verb is a promise about the design, and a reader who knows designs reads your verbs as a confession of how strong yours is.

The most common failure is not lying; it is drift. The abstract hedges correctly (“we document a robust association”), the introduction is a little bolder (“our results suggest that the program reduces the gap”), the results section forgets itself (“the program reduces the gap by 1.8 points”), and the conclusion goes all the way (“we have shown that fair-lending examinations cause a decline in discrimination”). Each step is small; the cumulative drift is a paper that claims far more than its design supports. Guard against drift with a deliberate pass: after a draft is done, read only the verbs attached to your main result, in every section, and force them all down to the level your weakest assumption permits. This is exactly the audit your Week-5 reading guides ran on published authors — the one where you underlined every causal verb and asked “did the design earn this?” Run it on yourself.

Hedge appropriately, but do not over-hedge into mush — that is the opposite failure. A paper drowning in “may possibly perhaps under certain conditions tentatively suggest” has hedged itself out of any claim at all, and a referee cannot tell what you are actually asserting. Calibration cuts both ways: claim exactly as much as your design supports, no more and no less. If you ran a clean DiD with flat pre-trends and a battery of passed robustness checks, you have earned a confident “the program reduced the gap, and this estimate is credible under parallel trends” — say it, plainly, with the assumption attached. The discipline is not timidity; it is precision.

8. Table and figure craft (and where the real standard lives)

Referees read tables before they read prose. You learned this as a consumer in Week 5 — go to the tables first, find the headline number, read the prose last and skeptically. As a producer, the implication is stark: your tables must stand alone, because they are read first and sometimes read only. A reader should be able to understand your main table — what the sample is, what the coefficient means, what the stars and the parenthetical numbers indicate, what fixed effects and clustering were used — without leaving the table to hunt through your prose. A table that requires the surrounding paragraphs to be intelligible is a table that fails its first and most important reader.

That self-containment comes from a small number of craft elements, and here I will state the principles and then point you, deliberately, to where the detailed standard lives. The principles: a table has an informative title and complete notes that define the sample, the units, the estimator, and every symbol; coefficients report standard errors or t-statistics in parentheses directly beneath them, with the flavor of standard error named (classical, HC1/HC2/HC3, HAC, clustered — and clustered on what); significance stars are defined in the notes, never left to the reader’s guess; numbers carry a consistent and sensible number of significant digits (a coefficient is not more precise for having six decimal places); and the fixed effects, controls, sample size, and within-R^2 are disclosed in dedicated rows so the reader can see the specification at a glance. Figures follow the same ethic: an event-study plot shows point estimates and confidence intervals, labels its axes in real units, marks the reference period, and is legible in grayscale.

The full standard — exact table layout, what belongs in notes versus the main text, how to report R^2 versus within-R^2, how many digits for which kind of number, the precise FE-and-cluster disclosure lines, the prose-style rules for hedging and citation — lives in Appendix D (book/appendices/D-style-guide/), and you should treat it as the binding spec for your manuscript. D.1 covers table layout and notes; D.2 covers which coefficients to report and the FE/cluster/sample disclosure; D.3 covers robustness sections and the threats-and-responses table; D.4 covers the replication packet; D.5 covers prose style and causal-language discipline. This chapter tells you why tables must stand alone and lead the results; Appendix D tells you exactly how to build one that does. Do not reinvent the standard here — point your manuscript at D and follow it. And do not hand-format your tables in a text editor: the notebook does it for you, which is where this chapter is headed.

9. A worked intro skeleton: Maya’s fair-lending DiD

Let us assemble the four moves of §2 into an actual introduction skeleton, for the project Maya has carried since Week 1 and whose identification memo you read in Ch 7.5: a staggered difference-in-differences asking whether state fair-lending examination programs reduced the county-level minority–white mortgage-denial gap, pointed at the HMDA data Prof. Gao and his coauthor used to study how same-sex couples were treated when they applied to borrow.¹ Read it as a fill-in-the-blanks template you can adapt to your own project; the bracketed labels name the move each paragraph is making.

[HOOK] In 2023, mortgage applicants in majority-minority neighborhoods were denied at nearly twice the rate of applicants in majority-white neighborhoods, a gap that narrows but does not vanish once income and loan size are held fixed. Whether such gaps reflect differential treatment by lenders — and whether supervisory policy can move them — is simultaneously a live question for fair-lending regulators and an unresolved empirical one, because the raw gap confounds how applicants are treated with who applies.

[CONTRIBUTION] This paper provides the first quasi-experimental estimate of how state fair-lending examination programs affect the county-level minority–white mortgage-denial gap, exploiting the staggered timing with which states adopted these programs as a source of plausibly exogenous variation in supervisory intensity.

[“WE FIND” PREVIEW] We find that adopting an examination program reduces the county-level denial gap by approximately 1.8 percentage points — about one-fifth of the pre-adoption gap — with effects emerging within two years of adoption and stabilizing thereafter. The estimate is robust to using only never- and not-yet-treated states as controls, to alternative clustering, and to a placebo test that randomly reassigns adoption years; pre-treatment event-study leads are flat and statistically indistinguishable from zero, consistent with the parallel-trends assumption on which our interpretation rests.

[POSITIONING, one bridge sentence into the literature] Our work sits at the intersection of two literatures that have not met: a descriptive HMDA literature that measures the denial gap but cannot separate treatment from composition, and an audit-study literature that isolates differential treatment but cannot speak to the population-scale effect of policy.

[ROADMAP] Section 2 positions our contribution in these literatures; Section 3 describes the HMDA sample and the construction of the denial gap; Section 4 presents the staggered difference-in-differences design and states our identifying assumption; Section 5 reports the main results; Section 6 presents robustness checks organized around the threats to identification; Section 7 concludes.

Read that skeleton against §3 and §7. The contribution sentence claims the “first quasi-experimental estimate” job and uses the verb “exploiting… plausibly exogenous variation” — a calibrated claim, not “we prove discrimination.” The preview gives the number, the magnitude in human units, the timing, and the key robustness fact, then immediately names the assumption it rests on (“consistent with the parallel-trends assumption”). The positioning sentence constructs the gap by contrast, not by listing. The hook leads with a fact and a tension, not with “the literature.” Every verb is bounded by the weakest assumption — parallel trends, untestable beyond the pre-period — so nowhere does the prose say “causes” without the conditional attached. That is the discipline of this entire chapter, compressed into five paragraphs. Your introduction will be longer and fuller, but if it makes these five moves, in this order, with verbs this honest, it will do its one job: promise a reader something worth their twenty minutes, and promise only what your design can deliver.

Your Turn

Open nb8.3 — “Publication-quality tables and figures.” This notebook takes the regression objects you produced in Chapters 8.1 and 8.2 — your pyfixest/linearmodels results, your event-study coefficients — and renders them into the publication-quality tables and figures your paper needs: a stargazer-style regression table and an event-study plot, both exported to LaTeX, both built to the Appendix D standard (named standard errors, defined stars, disclosed fixed effects and clustering, sensible significant digits, legible-in-grayscale figures). You will not hand-format a single table; the notebook does it, reproducibly, from the frozen results — which is the whole point. The tables you put in the paper are generated from the analysis, never retyped, so they can never silently drift from the numbers they claim to report.

Three reflection prompts to write up alongside the notebook:

Write your one-sentence contribution, then stress-test it. Hand it to a classmate who has not seen your project and ask them to tell you, from that sentence alone, what you did and why it matters. If they cannot, the sentence is failing the introduction’s central job. Which of the recognizable “jobs” from §3 does your contribution claim — first, overturn, reconcile, mechanism, new data — and does your literature review actually support that claim, or expose it?
Audit your verbs against your weakest assumption. Draft your “we find” preview paragraph. Now read only the verbs attached to your main result and force every one down to the level your weakest identifying assumption permits (§7). Did you write “causes” where “is associated with” was warranted? Did you over-hedge into mush where a confident, assumption-conditioned claim was earned? Rewrite until the verbs match the design exactly.
Make your headline table stand alone. Take the main table nb8.3 generates and cover up the surrounding prose. Can a reader who sees only the table determine the sample, the estimator, the meaning of the coefficient, what the stars mean, and what fixed effects and clustering were used? List every thing they cannot determine — then fix it in the table notes, following Appendix D, not in the paragraph.

Sun, H., & Gao, L. (2019). Lending practices to same-sex borrowers. Proceedings of the National Academy of Sciences, 116(19), 9293–9302.↩︎

# Chapter 8.3 — Writing the Empirical Paper (and the Abstract Your Poster Carries) You have, by now, almost everything a paper is made of. You filed a pre-analysis plan (Ch 7.3) and distilled it into the one page the whole project defends — the identification memo of Ch 7.5. You executed the pre-registered specification and built the specification curve (Ch 8.1). You ran column 3 of your threats table for every row, turning each promised defense into an actual robustness result (Ch 8.2). What you have is a folder full of tables, a frozen point estimate, a defensible identifying assumption, and a pile of checks that survived. What you do *not* yet have is a paper. This chapter is about the last transformation: turning that folder into a piece of prose that a stranger — a busy, skeptical, slightly hostile stranger called a referee — reads in one sitting and comes away *believing*. > **The ASSIP framing — what this chapter's prose discipline serves.** ASSIP's required terminal > deliverable is a **research poster** and a **JSSR abstract**, not a full paper (an optional > companion paper is available for students who want one — see Lab 8). This chapter is still the > binding prose-discipline standard for ASSIP, for two reasons. First, the **JSSR abstract** that > appears on your poster's title block and in the *Journal of Student-Scientists' Research* is a > 200–300-word miniature of the introduction this chapter teaches — the same four moves (hook, > contribution, "we find" preview, positioning bridge), the same one-sentence-contribution > discipline of §3, the same causal-language calibration of §7, compressed to ten sentences. The > abstract *is* an introduction at one-twentieth scale, and a chapter on writing an introduction is > a chapter on writing your JSSR abstract. Second, the **prose blocks on your poster** (the > question panel, the design panel, the contribution-and-limits panel — Ch 8.5 §1) are governed by > the same arguments-not-transcripts, headline-first, calibrated-verbs disciplines below. Read > this chapter as if you were writing a full paper — that is the only way to learn the shape — and > at the end of every section ask: *and what survives this rule when I compress it to one poster > panel or to one of ten abstract sentences?* The answers are in PS 8.3, which has been adapted > from a "write the introduction and results" assignment to a "write the JSSR abstract and the > poster's results narrative" assignment built on top of this chapter. Here is the reveal, the thing this whole chapter turns on, stated before the details so you carry it through everything that follows. **A paper is not a transcript of what you did; it is an argument for why a reader should believe what you found.** Those are different objects. The transcript is chronological and exhaustive — first I downloaded HMDA, then I cleaned it, then I tried three specifications, two of which broke. The argument is *logical* and *ruthlessly selective* — here is the question, here is why my design answers it, here is the answer, here is why you cannot easily dismiss it. Beginning writers produce transcripts and wonder why nobody finishes them. The move from transcript to argument is the single most valuable skill this chapter teaches, and almost every rule below is a special case of it. There is a second reveal layered under the first, and it is the reason Week 5 came before Week 8. You already know how to read a paper as a referee — tables first, identifying assumption second, prose last and skeptically. **Writing the paper is just building the object you learned to attack, so that it survives your own Week-5 reading.** Every section below maps onto a question your Reader's-Guide anatomy taught you to ask. The introduction answers "what is the question and why should I care?" The design section answers "what is the identifying assumption, and would it hold?" The results section answers "what is the headline number?" You are not learning a new format. You are learning to write for the reader you already are. --- ## 1. The shape of the paper Empirical-finance papers have a fixed skeleton, and the fixedness is a gift, not a constraint. A referee opening your manuscript knows exactly where to look for each thing, which means you do not get credit for being creative with the order — you only get penalized for hiding the introduction's contribution in section 4. The standard order is: **introduction, literature, data, empirical design / identification, results, robustness, conclusion**, with tables and figures threaded through results and robustness and the bibliography at the back. Top journals vary the labels (some fold literature into the introduction, some call the design section "empirical strategy" or "research design"), but the *load each section carries* is invariant. Learn the loads, not the labels. The proportions matter as much as the order. A common rookie error is a fifteen-page paper with a one-paragraph introduction and a six-page data section describing every variable in loving detail. Invert that instinct. The introduction is the most-read and most-rewritten part of the paper — many referees decide whether to recommend acceptance from the introduction alone, then read the rest looking for reasons to confirm that snap judgment. The data section, by contrast, should be efficient: enough that the work is reproducible, not so much that it buries the argument. Spend your writing time where the reader spends their attention, and the reader spends it at the front. One structural principle unifies the whole document: **say the important thing first, at every scale.** The paper leads with its contribution. The introduction leads with the hook. The results section leads with the headline table. Each paragraph leads with its topic sentence. A reader who quits after the first sentence of any unit should still have learned the most important thing in that unit. This is the opposite of how you were taught to write a mystery-novel essay in high school, building suspense toward a reveal at the end. In a paper, suspense is a bug. The reader is not your entertainment; they are your judge, and you make their job easy by front-loading every verdict. --- ## 2. The introduction that promises The introduction is a promise machine. In roughly four to six paragraphs it must make a specific reader want to read the rest, and it does that by promising — credibly — that the payoff is worth their next twenty minutes. There is a near-canonical structure that the best empirical papers follow almost mechanically, and you should follow it too until you have earned the right to deviate. It has four moves: **the hook, the one-sentence contribution, the "we find" preview, and the roadmap.** Take them in order. **The hook.** The first paragraph names the question and makes the reader care, in that order, fast. It opens with a real-world fact or tension — a number, a puzzle, a policy debate — not with "the literature has long studied." Maya's hook is not "fair lending has been studied since the 1970s." It is closer to: *In 2023, mortgage applicants from minority neighborhoods were denied at nearly twice the rate of applicants from white neighborhoods — a gap that persists even among applicants with similar incomes and loan sizes. Whether that gap reflects differential treatment, and whether policy can move it, is both a live regulatory question and an unresolved empirical one.* Two sentences and the reader knows the stakes are real, the question is contested, and an answer would matter. The hook earns the reader's attention with consequence, not with a literature recitation. **The one-sentence contribution.** This is the sentence everything else serves, and it deserves its own subsection below — for now, know that it lands in the first or second paragraph and says, in one sentence, *what this paper adds that did not exist before you wrote it.* Not what you did ("we run a difference-in-differences on HMDA") but what is now *known* that was not ("we provide the first causally credible estimate of how state fair-lending examination programs affect the minority–white mortgage-denial gap"). The difference between those two formulations is the difference between a paper that gets read and one that gets desk-rejected. **The "we find" preview.** Having promised a contribution, you must immediately pay a deposit on it: tell the reader the answer. A paragraph, usually beginning literally "We find that..." or "Our main result is...," that previews the headline number, its sign, its rough magnitude, and the key robustness fact. *We find that adopting a fair-lending examination program reduces the county-level minority–white denial gap by about 1.8 percentage points, roughly a fifth of the pre-period gap; the effect emerges within two years of adoption, is robust to alternative control groups and clustering, and survives a placebo test that randomly reassigns adoption years.* Students resist this. They feel they are "spoiling the ending." Reread §1: there is no ending to spoil. A referee who has to hunt through nine pages to find out what you found is a referee who is already annoyed with you. Give the number up front; you will spend the rest of the paper earning the right to have stated it. **The roadmap.** The introduction's last paragraph is a short, functional map: "Section 2 positions our work in the literature; Section 3 describes the HMDA data; Section 4 lays out the difference-in-differences design and our identifying assumption; Section 5 presents the main results; Section 6 reports robustness; Section 7 concludes." A few sentences, no drama. Some venues consider the explicit roadmap old-fashioned, but for a student paper it is a safe, professional default — it signals that you know the genre. A discipline that spans all four moves: **the introduction should be readable by someone who will never read the rest of the paper.** A program officer skimming fifty abstracts, a professor deciding whether to assign your paper, a journalist looking for a number to quote — all of them stop at the introduction. Write it so that a reader who stops there walks away with the question, the answer, and the appropriate degree of confidence. If your introduction only makes sense after one has read your results, it has failed at its one job. --- ## 3. The one-sentence contribution Stop and build this sentence on its own, because if you cannot write it, you do not yet have a paper — you have a regression and a hope, the same diagnosis the identification memo gave you about the identifying assumption. The **one-sentence contribution** is the answer to a question a skeptical reader is entitled to ask and will ask: *what is true now, that was not established before you did this work?* It is the reason the paper exists. Everything else — the data, the design, the forty robustness checks — is in service of making this one sentence believable, exactly as the whole paper is in service of the identifying-assumption sentence. The two sentences are cousins: one states what you claim to have found, the other states the condition under which the claim is true. A good contribution sentence usually does one of a small number of recognizable jobs, and naming the job helps you write the sentence. You might be the **first** to credibly estimate a specific effect ("we provide the first quasi-experimental estimate of..."). You might **overturn or qualify** an established finding ("we show that the widely cited X effect disappears once Y is accounted for"). You might **reconcile** two conflicting literatures, **measure a mechanism** the literature had only speculated about, or **bring new data** to an old question ("using transaction-level on-chain data, we..."). Pick the job honestly. The fastest way to a referee's contempt is a contribution sentence that claims the "first" job when three prior papers did the same thing, which is exactly what your literature review is about to either support or expose. Calibrate the verb to the evidence — this is the causal-language discipline of §7, previewed here because it bites first in this sentence. If your design is a clean staggered DiD with flat pre-trends, you have earned "credibly estimate." If your design is OLS on observables with a plausible omitted variable you could not rule out, you have not, and your contribution sentence says "document a robust association," "provide suggestive evidence," or "establish a new stylized fact" — never "show that X causes Y." The reading guides of Week 5 trained you to catch authors who overclaim in exactly this sentence. The grader of your paper is running the same check. Match the verb to the design, and run the check on yourself before anyone else does. A practical test: hand your one-sentence contribution to a classmate who has not seen your project and ask them to tell you, from that sentence alone, what you did and why it matters. If they can, the sentence works. If they ask "wait, what's the question?" or "is that causal?", the sentence is doing the introduction's whole job badly, and no amount of polish on paragraphs four through forty will fix it. --- ## 4. The literature review that positions Here is where most student papers go wrong, and the failure has a name: the **annotated bibliography.** That is the literature review that reads "Smith (2018) finds A. Jones (2020) finds B. Garcia (2021) finds C. We contribute to this literature." It is a list. It does the reader no work. It tells them what exists but not *where the hole is*, and the hole is the only thing the section exists to reveal. A list of prior work is to a literature review what a transcript is to a paper — the raw material, mistaken for the finished argument. A literature review does exactly one job: **it draws a map of what is known so that the gap you fill is visible as a gap.** The reader should finish the section able to point at empty space on the map and say "ah — *that* is what nobody has done, and that is what this paper does." You build that map by *grouping and contrasting*, not by enumerating. Cluster the prior work into two or three strands — by question, by method, or by finding — and characterize each strand by what it established *and what it could not.* "One strand documents the raw denial gap (Bartlett et al.; the HMDA descriptive literature) but cannot separate differential treatment from differential applicant composition. A second strand uses audit studies to isolate treatment but cannot speak to the population-scale effect of *policy*. We sit at the intersection: population-scale HMDA data *and* a policy shock that lets us identify a treatment effect." Now the gap is not asserted; it is *constructed*, brick by brick, out of the literature itself. Three rules keep the section honest and sharp. First, **every paper you cite should be load-bearing** — it either builds part of the map's wall or marks the edge of the hole. If a citation could be deleted without changing where the gap appears, delete it; a padded literature review signals that you are counting references rather than building an argument. Second, **be generous to the work you build on and precise about its limits, never dismissive.** "Prior work was wrong" is the voice of someone who has not read carefully and is about to be refereed by the author they just insulted. "Prior work established X under conditions Y; we extend to the case where Y fails" is the voice of someone who belongs in the conversation. Third, **position, do not summarize.** The reader does not need a book report on each paper; they need to know its coordinate on your map. One sentence per paper, often less, with the contrast doing the work. This section is also where Weeks 5 and 6 cash out. You read Fama–French, Jegadeesh–Titman, Petersen, Bertrand–Duflo–Mullainathan, the fair-lending and innovation literatures, precisely so you would know which conversations exist and where the live arguments are. A literature review is you reporting back from those conversations and announcing where you intend to speak. Cite primary sources with full bibliographic information per CONVENTIONS §6, and if you cannot verify a citation, tag it `[CHECK]` rather than fabricate it — a hallucinated reference is the one error a referee can catch in ten seconds and never forgive. --- ## 5. Data, design, and results These three sections are the body of the paper — the place where the promise of the introduction is redeemed with actual evidence. Each has a specific load to carry, and a specific failure mode to avoid. **The data section makes the work reproducible without burying the argument.** It names the source and vintage (HMDA LAR, a pinned snapshot date per CONVENTIONS §5), the sample (which years, which units, which filters and *why* each filter was applied — every exclusion is a potential selection threat, so disclose it), the unit of observation, and the construction of the key variables. It carries one near-mandatory artifact: a **summary-statistics table** (means, standard deviations, counts, by treatment status where relevant) that lets a reader sanity-check the sample before trusting anything built on it. What the data section does *not* do is narrate your cleaning ordeal. The reader does not need to know that the 2018 file had a malformed column; they need to know the final sample and how to rebuild it. Put the ordeal in the replication packet (Ch 8.5) and the appendix, not the paper. **The empirical design / identification section puts the identifying assumption front and center.** This section is, in large part, your Ch 7.5 identification memo turned into prose, and that is by design — the identifying-assumption paragraph you wrote there becomes this section nearly verbatim. State the specification in the CONVENTIONS §4 form: outcome, treatment, controls, fixed effects, clustering, sample, and **the identifying assumption in one sentence.** Write the estimating equation explicitly. For Maya, the staggered group-time formulation she committed to: $$ \text{Gap}_{ct} = \sum_{k \neq -1} \beta_k \,\mathbb{1}[t - G_s = k] + \boldsymbol{\delta}'\mathbf{X}_{ct} + \alpha_c + \lambda_t + \varepsilon_{ct}, $$ where $\text{Gap}_{ct}$ is the county-year minority–white denial gap, $G_s$ is the year state $s$ adopted its examination program, $\alpha_c$ and $\lambda_t$ are county and year fixed effects, and standard errors are clustered by state. Then — and this is the heart of the section — state the assumption that makes $\beta_k$ for $k \geq 0$ a causal effect rather than a correlation: *absent the programs, adopting and never-adopting states' denial gaps would have moved in parallel.* Name the threat, name the design feature that addresses it, in the same breath. This is CONVENTIONS §4 and the entire ethic of the identification memo, now load-bearing in the paper. A design section that says "we control for confounders" instead of naming the assumption has thrown away the one thing that makes the paper credible. **The results section leads with the headline table.** Open with the single table that contains your main estimate — for Maya, the overall ATT and the event-time profile from the clean Callaway–Sant'Anna estimator. Walk the reader through it in prose: point at the coefficient, state its sign, its magnitude *in units a human can feel* (1.8 percentage points, "a fifth of the pre-period gap" — not just a number), and its statistical precision. The cardinal sin here is the "data dump": a results section that presents eight tables with equal weight and lets the reader find the important one. You found it for them in the introduction; do it again here. Lead with the headline, interpret it economically (is the effect big enough to matter, not just big enough to be significant?), and only *then* present the supporting and secondary results. Significance is not the same as importance — a coefficient can be three-starred and economically trivial — and your prose must carry the economic interpretation that the stars cannot. --- ## 6. Robustness and conclusion **The robustness section converts your threats table into persuasion.** You already did the work in Chapter 8.2 — the placebos, the alternative standard errors, the bandwidth and control and sample perturbations, the Oster (2019) $\delta$ for selection on unobservables. The writing task is to *present* those checks as answers to the specific threats your design section raised, not as a context-free pile of extra regressions. The organizing move is to mirror the threats-and-responses table from your identification memo: each subsection of robustness takes one named threat and shows the check that addresses it, with the residual concern stated plainly. "A reader might worry that the result is driven by anticipation; we re-estimate excluding the year before adoption and the effect is unchanged (Table 5)." That sentence does three things — names the threat, reports the check, states the reassuring result — and it does them in the reader's order, the order in which they would *attack* the paper. Robustness sections that persuade are organized around the reader's doubts, not around the author's available regressions. Appendix D.3 gives the detailed standard for this; the principle is that a robustness check no one asked for persuades no one, while a check that answers a threat a referee was about to raise disarms the attack before it lands. **The conclusion says what we learned, what we cannot claim, and what comes next.** It is not a summary that repeats the introduction — the reader just read the paper; they do not need a recap. It is a *recalibration*. First, a tight restatement of the finding in its properly hedged form. Second — and this is the part students skip, to their cost — an honest statement of **limitations**: the residual concerns from your threats table, the populations your sample does not cover, the mechanism you measured an effect on but could not fully open up. The conclusion is where the residual-concern column of your identification memo finally appears in the paper's prose, and stating it is not weakness; it is the candor that makes a referee trust everything else. Third, "what's next": the question your paper opened but did not close, the natural extension, the data that would settle the residual concern. A conclusion that admits limits and points forward reads as the work of someone who sees their project clearly. A conclusion that claims the question is now permanently settled reads as the work of someone who has not yet been refereed. There is a temptation, in the conclusion, to let the verbs creep back up — to write "this paper proves" or "we have established that" after eleven pages of disciplined hedging. Resist it. The conclusion is the most-quoted part of the paper after the abstract, and a single overclaiming sentence there can undo the calibrated honesty of everything before it. --- ## 7. Causal-language discipline Run a thread back through every section above: the contribution sentence, the design section, the results, the conclusion all live or die on whether you matched your *verbs* to your *evidence*. This deserves its own treatment because it is the discipline most often broken and most ruthlessly punished, and because you have been trained to enforce it on others since Week 5. The rule is simple to state. **Your strongest verb is bounded by your weakest assumption.** A clean randomized experiment earns "causes," "increases," "the effect of." A quasi-experiment with a testable-and-passed identifying assumption (a DiD with flat pre-trends, an RD with a smooth density) earns "causally estimate," "the program reduced," with the assumption named. An observational regression on observables — OLS with a plausible omitted variable you could not rule out — earns only "is associated with," "predicts," "is consistent with," "suggestive of." A descriptive or predictive study (Sam's momentum sort, Fama–French) earns "documents," "captures variation in," and must *not* be dressed in causal clothing at all. The verb is a promise about the design, and a reader who knows designs reads your verbs as a confession of how strong yours is. The most common failure is not lying; it is *drift*. The abstract hedges correctly ("we document a robust association"), the introduction is a little bolder ("our results suggest that the program reduces the gap"), the results section forgets itself ("the program reduces the gap by 1.8 points"), and the conclusion goes all the way ("we have shown that fair-lending examinations cause a decline in discrimination"). Each step is small; the cumulative drift is a paper that claims far more than its design supports. Guard against drift with a deliberate pass: after a draft is done, read *only* the verbs attached to your main result, in every section, and force them all down to the level your weakest assumption permits. This is exactly the audit your Week-5 reading guides ran on published authors — the one where you underlined every causal verb and asked "did the design earn this?" Run it on yourself. Hedge appropriately, but do not over-hedge into mush — that is the opposite failure. A paper drowning in "may possibly perhaps under certain conditions tentatively suggest" has hedged itself out of any claim at all, and a referee cannot tell what you are actually asserting. Calibration cuts both ways: claim *exactly* as much as your design supports, no more and no less. If you ran a clean DiD with flat pre-trends and a battery of passed robustness checks, you have earned a confident "the program reduced the gap, and this estimate is credible under parallel trends" — say it, plainly, with the assumption attached. The discipline is not timidity; it is precision. --- ## 8. Table and figure craft (and where the real standard lives) Referees read tables before they read prose. You learned this as a *consumer* in Week 5 — go to the tables first, find the headline number, read the prose last and skeptically. As a *producer*, the implication is stark: **your tables must stand alone**, because they are read first and sometimes read *only.* A reader should be able to understand your main table — what the sample is, what the coefficient means, what the stars and the parenthetical numbers indicate, what fixed effects and clustering were used — without leaving the table to hunt through your prose. A table that requires the surrounding paragraphs to be intelligible is a table that fails its first and most important reader. That self-containment comes from a small number of craft elements, and here I will state the *principles* and then point you, deliberately, to where the detailed standard lives. The principles: a table has an informative **title** and complete **notes** that define the sample, the units, the estimator, and every symbol; coefficients report **standard errors or t-statistics** in parentheses directly beneath them, with the flavor of standard error named (classical, HC1/HC2/HC3, HAC, clustered — and clustered *on what*); **significance stars** are defined in the notes, never left to the reader's guess; numbers carry a **consistent and sensible number of significant digits** (a coefficient is not more precise for having six decimal places); and the **fixed effects, controls, sample size, and within-$R^2$** are disclosed in dedicated rows so the reader can see the specification at a glance. Figures follow the same ethic: an event-study plot shows point estimates *and* confidence intervals, labels its axes in real units, marks the reference period, and is legible in grayscale. The full standard — exact table layout, what belongs in notes versus the main text, how to report $R^2$ versus within-$R^2$, how many digits for which kind of number, the precise FE-and-cluster disclosure lines, the prose-style rules for hedging and citation — lives in **Appendix D** (`book/appendices/D-style-guide/`), and you should treat it as the binding spec for your manuscript. D.1 covers table layout and notes; D.2 covers which coefficients to report and the FE/cluster/sample disclosure; D.3 covers robustness sections and the threats-and-responses table; D.4 covers the replication packet; D.5 covers prose style and causal-language discipline. This chapter tells you *why* tables must stand alone and lead the results; Appendix D tells you *exactly how* to build one that does. Do not reinvent the standard here — point your manuscript at D and follow it. And do not hand-format your tables in a text editor: the notebook does it for you, which is where this chapter is headed. --- ## 9. A worked intro skeleton: Maya's fair-lending DiD Let us assemble the four moves of §2 into an actual introduction skeleton, for the project Maya has carried since Week 1 and whose identification memo you read in Ch 7.5: a staggered difference-in-differences asking whether state fair-lending examination programs reduced the county-level minority–white mortgage-denial gap, pointed at the HMDA data Prof. Gao and his coauthor used to study how same-sex couples were treated when they applied to borrow.[^gaosun] Read it as a fill-in-the-blanks template you can adapt to your own project; the bracketed labels name the move each paragraph is making. > **[HOOK]** In 2023, mortgage applicants in majority-minority neighborhoods were denied at nearly twice the rate of applicants in majority-white neighborhoods, a gap that narrows but does not vanish once income and loan size are held fixed. Whether such gaps reflect differential treatment by lenders — and whether supervisory policy can move them — is simultaneously a live question for fair-lending regulators and an unresolved empirical one, because the raw gap confounds how applicants are *treated* with who *applies*. > > **[CONTRIBUTION]** This paper provides the first quasi-experimental estimate of how state fair-lending examination programs affect the county-level minority–white mortgage-denial gap, exploiting the staggered timing with which states adopted these programs as a source of plausibly exogenous variation in supervisory intensity. > > **["WE FIND" PREVIEW]** We find that adopting an examination program reduces the county-level denial gap by approximately 1.8 percentage points — about one-fifth of the pre-adoption gap — with effects emerging within two years of adoption and stabilizing thereafter. The estimate is robust to using only never- and not-yet-treated states as controls, to alternative clustering, and to a placebo test that randomly reassigns adoption years; pre-treatment event-study leads are flat and statistically indistinguishable from zero, consistent with the parallel-trends assumption on which our interpretation rests. > > **[POSITIONING, one bridge sentence into the literature]** Our work sits at the intersection of two literatures that have not met: a descriptive HMDA literature that measures the denial gap but cannot separate treatment from composition, and an audit-study literature that isolates differential treatment but cannot speak to the population-scale effect of policy. > > **[ROADMAP]** Section 2 positions our contribution in these literatures; Section 3 describes the HMDA sample and the construction of the denial gap; Section 4 presents the staggered difference-in-differences design and states our identifying assumption; Section 5 reports the main results; Section 6 presents robustness checks organized around the threats to identification; Section 7 concludes. Read that skeleton against §3 and §7. The contribution sentence claims the "first quasi-experimental estimate" job and uses the verb "exploiting... plausibly exogenous variation" — a calibrated claim, not "we prove discrimination." The preview gives the number, the magnitude in human units, the timing, *and* the key robustness fact, then immediately names the assumption it rests on ("consistent with the parallel-trends assumption"). The positioning sentence constructs the gap by contrast, not by listing. The hook leads with a fact and a tension, not with "the literature." Every verb is bounded by the weakest assumption — parallel trends, untestable beyond the pre-period — so nowhere does the prose say "causes" without the conditional attached. That is the discipline of this entire chapter, compressed into five paragraphs. Your introduction will be longer and fuller, but if it makes these five moves, in this order, with verbs this honest, it will do its one job: promise a reader something worth their twenty minutes, and promise only what your design can deliver. --- ## Your Turn Open **nb8.3 — "Publication-quality tables and figures."** This notebook takes the regression objects you produced in Chapters 8.1 and 8.2 — your `pyfixest`/`linearmodels` results, your event-study coefficients — and renders them into the publication-quality tables and figures your paper needs: a `stargazer`-style regression table and an event-study plot, both exported to LaTeX, both built to the Appendix D standard (named standard errors, defined stars, disclosed fixed effects and clustering, sensible significant digits, legible-in-grayscale figures). You will not hand-format a single table; the notebook does it, reproducibly, from the frozen results — which is the whole point. The tables you put in the paper are *generated* from the analysis, never retyped, so they can never silently drift from the numbers they claim to report. Three reflection prompts to write up alongside the notebook: 1. **Write your one-sentence contribution, then stress-test it.** Hand it to a classmate who has not seen your project and ask them to tell you, from that sentence alone, what you did and why it matters. If they cannot, the sentence is failing the introduction's central job. Which of the recognizable "jobs" from §3 does your contribution claim — first, overturn, reconcile, mechanism, new data — and does your literature review actually support that claim, or expose it? 2. **Audit your verbs against your weakest assumption.** Draft your "we find" preview paragraph. Now read *only* the verbs attached to your main result and force every one down to the level your weakest identifying assumption permits (§7). Did you write "causes" where "is associated with" was warranted? Did you over-hedge into mush where a confident, assumption-conditioned claim was earned? Rewrite until the verbs match the design exactly. 3. **Make your headline table stand alone.** Take the main table nb8.3 generates and cover up the surrounding prose. Can a reader who sees *only* the table determine the sample, the estimator, the meaning of the coefficient, what the stars mean, and what fixed effects and clustering were used? List every thing they cannot determine — then fix it in the table notes, following Appendix D, not in the paragraph. [^gaosun]: Sun, H., & Gao, L. (2019). Lending practices to same-sex borrowers. *Proceedings of the National Academy of Sciences*, 116(19), 9293–9302.